Asymptotic Analysis Of Transonic Steady-state Solution For Hydrodynamic Semiconductor Models

In this paper,we study the asymptotic situation of the transonic steady state solution under the influence of quasi-neutral limit and relaxation limit in the case of isentropic unipolar.The article mainly introduces the transonic solution of semiconductor HD model from three cases Analysis,research methods and results are as follows:Case 1: When the Debye length is approaching zero,the method of telescopic transformation is used to obtain a steady-state equation without semiconductor effect.There is always a transonic solution;when there is a semiconductor effect,for a fixed span,the equation is analyzed only with a phase diagram Transonic solution;Case 2:When the relaxation limit approaches zero,the energy estimation method is used to prove that for a fixed span,the equation has only a subsonic solution;Case 3: When the two limit cases are coupled,the transonic solution is determined by the two The ratio is determined,because the analysis is more complicated,the paper only takes the special ratio to get the steady-state equation and only has the transonic solution.There is no definite conclusion for the more comprehensive situation.This study can be used to continue to investigate the semiconductor HD model.The quasi-neutral limit problem provides some references.